Mud Bed Removal and New Floor

I am renovating my 2nd story guest bathroom in a 1911 house. The original installation was mosaic tile set in a roughly 4" thick mud bed. The tile and concrete had become cracked and deteriorated over time so I have removed the tile and concrete down to the joists (16" oc and they have been hatcheted). Between the joists, running perpendicular, there are 1x6" planks sitting on cleats 4" below the top of the joists that supported the concrete bed. I plan on installing a plywood subfloor, ditra and ceramic tile as the new floor. My questions on how to proceed are as follows:

1. Should I remove the 1x6" planks and cleats and sister the joists up to the desired height? Or can I build up off of the 1x6" planks? My concern is that the mud bed previously ran under (about 6") and supported the skirt of my cast iron tub (the tub is temporarily supported on 2x4s sitting on the 1x6 planks). It would be easier to place supports off of the planks for the new floor because I can't get under the tub to the last joist, however the planks were obviously not intended to be used this way. They are sound and happen to be there though so why not?

2. Concerning the new floor, I've read many different opinions on the proper subfloor and underlayment for ceramic tile. I see a total subfloor thickness of 1'-1/8" a lot. Is this the thickness of the plywood layers alone or does it include the cement board layer as well? I thought 3/4" plywood was fine for structural purposes so I'm confused as to why another 3/8" layer is necessary. So, if I am using Ditra instead of cement board can I simply have a 3/4" plywood subfloor, modified thinset, Ditra, unmodified thinset, then tile?